Random Walks, Conductance, and Resistance for the Connection Graph Laplacian

2023/08/18 by Alexander Cloninger, Cloninger, Alexander, Gal Mishne +9 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph theory and applications #Molecular Junctions and Nanostructures

paper · pdf · doi:10.48550/arxiv.2308.09690

openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of Dirichlet-type and Poisson-type problems on connection graphs. Additionally, we delve into random walks, taking into account both node transitions and vector rotations. This approach introduces novel concepts of effective conductance and resistance matrices for connection graphs, capturing mean rotation matrices corresponding to random walk transitions. Thereby, it provides new theoretical insights for network analysis and optimization.

Cited by

• Yang-Mills Meets Data
• Powers of Magnetic Graph Matrix: Fourier Spectrum, Walk Compression, and Applications
• Repelling curvature via ε-repelling Laplacian on positive connected signed graphs

Related

• Electrical Networks with Prescribed Current and Applications to Random\n Walks on Graphs
• Kron Reduction and Effective Resistance of Directed Graphs
• Random Electrical Networks on Complete Graphs II: Proofs
• The random conductance model with heavy tails on nested fractal graphs
• Resistance Distances in Directed Graphs: Definitions, Properties, and Applications